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General Relativity and Cosmology

Module PH2043

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2022/3 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2022/3WS 2021/2WS 2020/1WS 2019/20WS 2018/9WS 2017/8SS 2011

Basic Information

PH2043 is a semester module in English or German language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
300 h 90 h 10 CP

Responsible coordinator of the module PH2043 is Alejandro Ibarra.

Content, Learning Outcome and Preconditions


  1. Review of Special Relativity
  2. Manifolds.
  3. The Equivalence Principle and Spacetime Curvature.
  4. Gravitation.
  5. The Schwarzschild Geometry and Black Holes.
  6. Gravitational radiation.
  7. Cosmology.

    Learning Outcome

    After participation in the Module the student is able to:

    1. Understand the origin of gravity as the effect of the curvature of spacetime.
    2. Describe the classical experimental tests of general relativity: the deflection of light, the precession of perihelia and gravitational redshift.
    3. Understand the basic physics of black holes.
    4. Understand the basic properties of gravitational waves.
    5. Describe the different stages of the expanding Universe and derive the Hubble’s law.


    No prior knowledge necessary, beyond the admission requirements for the master's degree.

    Courses, Learning and Teaching Methods and Literature

    Courses and Schedule

    VU 6 General Relativity and Cosmology Ibarra, A. Mon, 12:00–14:00, PH HS3
    Tue, 08:00–10:00, PH HS3
    and dates in groups

    Learning and Teaching Methods

    This module consists of a lecture and an exercise course.

    The lecture is designed for the presentation of the subject, usually by blackboard presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problems, which cover important aspects of the field.

    In the exercise course the learning content is deepened and exercised using problem examples, developing the analytic skills of the students and their ability to perform calculations. The homework problems are discussed in the exercise by the students themselves under the supervision of a tutor in order to develop the skills to explain a physics problem logically.


    Lecture, blackboard, problem sets, presentation, homework problems and their discussion in tutorial groups.


    • S. Caroll: Spacetime and Geometry, Pearson, (2013)
    • S. Weinberg: Gravitation and Cosmology, Wiley, (1972)
    • E.W. Kolb & M.S. Turner: The Early Universe, Westview Press, (1994)

    Module Exam

    Description of exams and course work

    There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

    For example an assignment in the exam might be:

    • Calculate trajectories of light or massive objects around a star
    • Determine the evolution of a Universe with a certain energy content.

    In the exam no learning aids are permitted.

    Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

    There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of passing the voluntary test exam during the semester

    Exam Repetition

    The exam may be repeated at the end of the semester.

    Current exam dates

    Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

    Exam to General Relativity and Cosmology
    Mon, 2024-03-25, 11:00 till 14:00 2502
    till 2024-03-21
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